How to measure specific heat using event-by-event average pT fluctuations

A simple way to visualize event-by-event average pT fluctuations is by assuming that each collision has a different temperature parameter (inverse pT slope) and that the ensemble of events has a temperature distribution about the mean, less than T greater than , with standard deviation sigmaT. PHENIX characterizes the non-random fluctuation of MpT, the event-by-event average pT, by FpT, the fractional difference of the standard deviation of the data from that of a random sample obtained with mixed events. This can be related to the temperature fluctuation: FpT = sigmaMpTdata/sigmaMpTrandom - 1 ~ (less than eta greated than-1)sigmaT 2/ less thanT greated than 2. Combining this with the Gavai et al. [5] and Korus et al. [6] definitions of the specific heat per particle, a simple relationship is obtained: cv/T3 = less than eta greated than/less than Ntot greated than )Ĺ(1/FpT). FpT is measured with a fraction less than eta greated than)Ntot* of the total particles produced, a purely geometrical factor representing the fractional acceptance, ~1/33 in PHENIX. Gavai et al. [5] predict that cv/T3 = 15, which corresponds to FpT ~ 0.20% in PHENIX, which may be accessible by measurements of MpT in the range 0.2 d pT d 0.6 GeV/c. In order to test the Gavai et al. prediction that cv/T3 is reduced in a QGP compared to the ideal gas value (15 compared to 21), precision measurements of FpT in the range 0.20% for 0.2 less-than or equal to pT greater-than or equal to 0.6 GeV/c may be practical.